Problem: Solve for $x$ and $y$ using elimination. ${6x-4y = -4}$ ${-5x-5y = -55}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-4$ ${30x-20y = -20}$ $20x+20y = 220$ Add the top and bottom equations together. $50x = 200$ $\dfrac{50x}{{50}} = \dfrac{200}{{50}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {6x-4y = -4}\thinspace$ to find $y$ ${6}{(4)}{ - 4y = -4}$ $24-4y = -4$ $24{-24} - 4y = -4{-24}$ $-4y = -28$ $\dfrac{-4y}{{-4}} = \dfrac{-28}{{-4}}$ ${y = 7}$ You can also plug ${x = 4}$ into $\thinspace {-5x-5y = -55}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 5y = -55}$ ${y = 7}$